Sang-Gu Lee

Sang-Gu Lee
Sungkyunkwan University | SKKU ·  Department of Mathematics

PhD

About

162
Publications
110,119
Reads
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776
Citations
Additional affiliations
September 2006 - July 2007
University of Northern Iowa
Position
  • Visiting Prof.
Description
  • Research
December 1998 - August 1999
Utah State University
Position
  • Visiting Prof.
September 1998 - December 1998
College of William and Mary
Position
  • Visiting Prof.
Description
  • Research~~

Publications

Publications (162)
Book
Full-text available
Calculus with Sage, Sang-Gu Lee with Eung-Ki Kim, Yoonmee Ham, Ajit Kumar, Robert Beezer, Quoc-Phong Vu, Lois Simon, Suk-Geun Hwang, (KyungMoonSa), March. 5, 2014. ISBN 978-89-6105-458-4 . (In English), http://matrix.skku.ac.kr/Cal-Book/
Book
Full-text available
[빅북] 선형대수학, 이상구 with 이재화, 김경원, ISBN 978-89-24-01524-9, 교보문고 POD (2014. 9. 12.) [Big Book] Linear Algebra (Free e-book)
Book
Full-text available
Pioneers of Korean Modern Mathematics (한국근대수학의 개척자들), 이상구 assisted by 이재화, ISBN 978-89-7986-984-2 (03410), 사람과 무늬 (2013. 5.10.) http://matrix.skku.ac.kr/K-Math-History/index.htm
Book
Full-text available
나카다 노리오 지음 ; 이상구,김호순 [공]옮김 중전기부 仲田紀夫, 1925-. 이상구, 김호순 서울 : 경문사, 2011. 216 p. : 삽화 ; 23 cm. 「社会数学」400年の波乱万丈! ISBN 9788961053891 분류번호 510.2
Book
Full-text available
This book, ‘Linear Algebra with Sage’, has two goals. The first goal is to explain Linear Algebra with the help of Sage. Sage is one of the most popular computer algebra system(CAS). Sage is a free and user-friendly software. Whenever the Sage codes are possible, we illustrate examples with Sage codes. The second goal is to make the book accessibl...
Conference Paper
Reservoir Computing (RC) is an effective approach to design and train recurrent neural networks , which is successfully and widely applied in time series prediction tasks. Echo state network (ESN) is one of the most well-known types of reservoir computing because of its outstanding performance to a wide range of real-world applications. However, th...
Book
Full-text available
I. Basic Math for AI 1. Function, Graph and Solution of Equations II. Artificial Intelligence and Matrix 2. Data and Matrices 3. Classification of Data 4. Solution Sets for System of Linear Equations 5. Orthogonal Projection and Least Squares Problem 6. Matrix decompositions (LU, QR, SVD) III. AI and Optimal solution (Calculus) 7. Limits of Funct...
Book
Full-text available
(English version) Textbook [K-MOOC] Introductory Math for Artificial Intelligence http://matrix.skku.ac.kr/intro-math4AI/
Article
Full-text available
Problem/Project based learning(PBL) is a student-centered teaching method in which students collaboratively solve problems and reflect their experiences. According to the results of PBL study and the experiences of the authors in PBL instruction, this paper introduced the necessities, output and significance of learning process PBL evaluation metho...
Research
Full-text available
Problem/Project based learning(PBL) is a student-centered teaching method in which students collaboratively solve problems and reflect their experiences. According to the results of PBL study and the experiences of the authors in PBL instruction, this paper introduced the necessities, output and significance of learning process PBL evaluation metho...
Book
Full-text available
Introductory Math for Artificial Intelligence(인공지능을 위한 기초수학 입문) 생산 가능 인구의 감소 등 사회 구조 및 고용 환경이 빠르게 변화하고 있다. 이러한 변화의 하나로서, 인공지능(Artificial Intelligence, AI)의 비약적인 발전을 들 수 있다. 은 인공지능이 어떤 수학적 원리로 작동하는지를 이해하는데 필요한 기본적인 수학을 고등학교 1학년 정도의 수학 지식을 갖춘 일반인은 누구라도 쉽게 관련된 행렬, 도함수, 통계 내용을 이해하고 실습할 수 있도록 서술하였다. 인공지능이란 인간처럼 사고하는 시스템을 말한다. 현재 인공지능은 우리가 느끼지 못하는 사이에 우...
Article
We investigated deep image‐to‐image regression models to retrieve diffracted and/or defocused images induced from optical components. For the purpose, a quantitative metric for strength of diffraction/defocus and optical simulation method have been devised. The quality of retrieved images has been improved by optimizing optical components, and by m...
Article
Full-text available
Today’s healthcare, intelligent robots, smart home systems, and car sharing are already innovating with cutting-edge information and communication technologies such as Artificial Intelligence (AI), the Internet of Things, the Internet of Intelligent Things, and Big data. It is deeply affecting our lives. In the factory, robots have been working for...
Article
Full-text available
Purpose: Study purpose was to describe the child safety injury experiences, injury prevention behaviors and educational needs of immigrant Vietnamese women on Jeju Island, and to explore associations among those factors. Methods: A descriptive correlational study was conducted using structured questionnaires to collect data from immigrant Vietna...
Chapter
Full-text available
『인공지능을 위한 기초수학 』 Ch. 1 행렬과 데이터
Article
Full-text available
Recently, Furtula et al. [B. Furtula, I. Gutman, S. Ediz, On difference of Zagreb indices, Discrete Appl. Math., 2014] introduced a new vertex-degree-based graph invariant "reduced second Zagreb index" in chemical graph theory. Here we generalize the reduced second Zagreb index (call "general reduced second Zagreb index"), denoted by GRM(G) and is...
Book
Full-text available
New version (Sep. 1, 2018) of < Linear Algebra (선형대수학) e- book > written by Sang-Gu LEE with Jon-Lark KIM, In-Jae KIM, Namyong LEE, Ajit KUMAR, Phong VU, Victoria LANG, Jae Hwa LEE
Article
Full-text available
This article deals with the authors' experiences with flipping a basic undergraduate mathematics course in Introductory Linear Algebra, including the platform for flipping a classroom and students' feedbacks. Contrary to a traditional class where students typically come to the classroom unprepared, in a flipped classroom, students are asked to read...
Presentation
Full-text available
Math for Big Data / Machine Learning / AL
Book
Full-text available
70 Years History of Korean Mathematical Society , 대한수학회 70년사
Presentation
Full-text available
Math for Big Data, Part 2
Article
Full-text available
History of Korean Math Society
Presentation
Full-text available
Math for Big Data, Part 1
Article
Full-text available
Since modern mathematics textbooks were introduced in the late 19th century Korea, arithmetic experts started to teach modern mathematics using Arabic numerals at village schools and churches. After the Gabo Education Reform of 1894, western mathematics education was included in public education and the mathematics textbooks began to be officially...
Article
Full-text available
Recently an extensive study of the mathematicians who have overcome the visually impaired and contribute to the academic in math was published. In the case of Korea, we can find there are mathematicians who have overcome physical disabilities such as cerebral palsy and polio. However there is no example of blind person who majored mathematics to be...
Article
Full-text available
This study deals with the content that was developed by the authors and the utilization of the `Interactive Engineering Math Laboratory (IEmath Lab).` IEmath Lab provides online review lectures as well as a wide range of examples and exercises from the curriculum of engineering mathematics courses. The lectures come with pre-coded Python-based Sage...
Book
Full-text available
그동안 기존의 수학 관련 저서들을 충분히 이해하기 위해서는 상당한 수학적 지식이 필요했으며, 전문 수학자가 아니면 다소 어려움과 불편함이 따른다는 점이 있었다. 때문에 수학을 전공하지 않은 일반 독자가 문화 속에서 수학을 이해하기에는 다소 어려움이 있었던 것이 사실이다. 그러므로 이 책은 그러한 어려움을 조금이나마 해소할 수 있는 ‘문화 속의 수학’을 지향하면서 기획되었다. 미술, 음악, 디자인, 건축, 철학, 문학, 역사, 암호, 스포츠, 게임 그리고 영화까지 각 문화별로 수학에 대해 쉽게 접근할 수 있도록 구성되어 있는 책이다.
Article
Full-text available
We consider a bistable attraction-repulsion chemotaxis system in one dimension. The study in this paper asserts that conditions for chemotactic coefficients for attraction and repulsion to show existence of stationary solutions and Hopf bifurcation in the interfacial problem as the bifurcation parameters vary are obtained analytically.
Article
Full-text available
We had a full scale of literature survey and case survey of mathematics Flipped Learning class models. The purpose of this study is to design and adopt a Flipped Learning `Linear Algebra` class model that fis our need. We applied our new model to 30 students at S University. Then we analyzed the activities and performance of students in this course...
Book
Full-text available
공학계열 학생을 위한 공학수학 교재로서, 미분방정식에서부터 복소함수에 이르기까지 공학계열 학생이라면 알아야 할 내용들을 두 권에 걸쳐 다룬다. 책에 수록된 정의, 정리, 예제를 통해 수학적 이론을 다룬 뒤 관련 예제를 풀고, 필요에 따라 Sage 연산 도구를 사용하는 과정을 담아 학습한 내용을 시각화하거나 복잡한 계산을 해볼 수 있다. 이 책에서는 복잡한 계산을 대신해주는 Sage 도구를 활용하고 있어서 반복되는 문제 풀이가 아닌 공학수학의 개념 토론에 더 많은 시간을 쓸 수 있게 했다. 특히 예제와 연습문제를 위해 작성된 Sage 코드는 온라인 실습실을 통해서도 제공하고 있어 직접 실습이 가능하며, 무료로 제공되는 장...
Book
Full-text available
공학계열 학생을 위한 공학수학 교재로서, 미분방정식에서부터 복소함수에 이르기까지 공학계열 학생이라면 알아야 할 내용들을 두 권에 걸쳐 다룬다. 책에 수록된 정의, 정리, 예제를 통해 수학적 이론을 다룬 뒤 관련 예제를 풀고, 필요에 따라 Sage 연산 도구를 사용하는 과정을 담아 학습한 내용을 시각화하거나 복잡한 계산을 해볼 수 있다. 이 책에서는 복잡한 계산을 대신해주는 Sage 도구를 활용하고 있어서 반복되는 문제 풀이가 아닌 공학수학의 개념 토론에 더 많은 시간을 쓸 수 있게 했다. 특히 예제와 연습문제를 위해 작성된 Sage 코드는 온라인 실습실을 통해서도 제공하고 있어 직접 실습이 가능하며, 무료로 제공되는 장...
Article
Full-text available
It is well known that not all sign idempotent sign pattern matrices allow idempotence. In this paper, we found a necessary and sufficient condition for a sign idempotent sign pattern matrix to allow idempotence. In addition, we investigated the nonnegativity of sign idempotent sign pattern matrices that allow idempotence. Finally, we show that if A...
Article
Full-text available
This study is to find out a way to foster self-directed learning math skills for the low-income youth at child care centers. Taking advantage of EBS materials, we found the youth, low-income youth in particular, were positively influenced to learn mathematics in the way of self-directed and action learning. This program gives a model of the self-di...
Article
Full-text available
In this paper, we introduce development process and application of a simple and effective model of a statistics laboratory using open source software R, one of leading language and environment for statistical computing and graphics. This model consists of HTML files, including Sage cells, video lectures and enough internet resources. Users do not h...
Book
Full-text available
<19장 수학과 컴퓨팅 사고력(CT), 성균관대학교 이상구 ·368-386> 80년대 학교현장에 소형 개인용 컴퓨터와 휴대용 계산기가 보급되면서 수학수업을 포함한 수학교육의 실제에서 이런 기술공학 도구의 활용에 대한 연구가 시작되었다전미수학교사협의회(NCTM)은 1984년 연보로서《수학교육에서 컴퓨터 (Computers in Mathematics Education)》를 출간하였고, 1992년에는 수학교육에서 계산기 (Calculators in Mathematics Education)》를 출간하였다. 이 사이에 그들은 1989년 학교수학에서 교육과정과 평가의 새로운 방향》이라는 규준집을 발간하면서 그 발간의 배경의 하...
Book
Full-text available
This book, (The 2nd Version) ‘Linear Algebra with Sage’, has two goals. The first goal is to explain Linear Algebra with the help of Sage. Sage is one of the most popular computer algebra system(CAS). Sage is a free and user-friendly software. Whenever the Sage codes are possible, we illustrate examples with Sage codes. The second goal is to make...
Patent
특허등록번호 : 10-1560802, 성대관리번호 : [국내) R-2014-0340-KR-1] , 특허 출원일 2014-10-15 -출원번호 : 10-2014-0139027. 발명의명칭 : 임의 수학 문제를 제공하는 클라우드 컴퓨팅 서버, 방법 및 기록매체 , 발명자 : 이상구외 * 등록 번호 확정일 : 2015-10-07 (특허법인 엠에이피에스)
Article
Full-text available
There are lots of disabled mathematicians who overcame their disabilities and made great achievement to the world of mathematics. In this article, we introduce disabled mathematicians who overcome their disabilities and contributes to the development of mathematics: Nicholas Saunderson, Leonhard Euler, Lewis Carroll, Solomon Lefschetz, Louis Antoin...
Book
Full-text available
2nd Edition, Bigbook Linear Algebra, 빅북 선형대수학, 개정판 New Version, July, 2015, e-book
Data
[Book] Mathematics: Form and Function - Translation (수학: 형식과 기능)
Data
Full-text available
Chapter7 Linear Algebra of the book [Mathematics: Form and Function] - Translation (수학: 형식과 기능)
Article
Full-text available
In this paper, we give answers to some interesting questions about a Confucian scholar and mathematician in the late Joseon Dynasty, CHOI Seok-Jeong(崔錫鼎, 1646–1715), who was inducted into the Science and Technology Hall of Fame (http: //kast.or.kr/HALL) for his mathematical achievements in October, 2013. In particular, we discover that CHOI Seok-Je...
Article
Full-text available
3D-Printing is one of the most innovative technologies that will be widely used in the 21st century. 3D-Printing also serves as an indispensable tool in STEAM education. In this article, we introduce what we have done in our mathematical modeling class in Uni. and recent R&E project under the support of Korean Foundation for the Advancement of Scie...
Article
Full-text available
Recently in major industrial areas, there has been a rapidly increasing demand for ‘Computational Thinking’, which is integrated with a computer’s ability to think as a human world. Developed countries in the last 20 years naturally have been improving students’ computational thinking as a way to solve math problems with CAS in the areas of mathema...
Article
Full-text available
3D-Printing is one of the most innovative technologies that will be widely used in the 21st century. 3D-Printing also serves as an indispensable tool in STEAM education. In this article, we introduce what we have done in our mathematical modeling class in Uni. and recent R&E project under the support of Korean Foundation for the Advancement of Scie...
Data
Full-text available
Article
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Recently, with the development of technology, intuitive understanding of abstract mathematical concepts through visualizations is growing in popularity within college mathematics. In this study, we introduce free visualization tools developed for better understanding of topics which students learn in Calculus. We visualize important concepts of Cal...
Article
Full-text available
Recently, the widespread usage of 3D-Printing has grown rapidly in popularity and development of a high level technology for 3D-Printing has become more necessary. Given these circumstances, effectively using mathematical knowledge is required. So, we have developed free web tools for 3D-Printing with Sage, for mathematical 3D modeling and have uti...
Article
Full-text available
In this paper, we introduce the history and the present status of the Mathematics Genealogy Project (MGP). The cases of David Hilbert and the first author were used to show how it works. As an example, we explain how to gain useful information such as the granting year of mathematics Ph. D degree holders, the title of dissertation, advisors and des...
Conference Paper
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Math is Ubiquitous in Seoul, ICM 2014 Newsletter Aug. 21, 2014,
Article
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While the usage of powerful mathematics software packages plays a key role in calculus, linear algebra, and higher level mathematics courses, shortcomings in these softwares exist, namely, issues of price and portability. A free online function and calculus concept grapher has been developed using Sage, a mathematics software based primarily on the...
Article
Full-text available
The present study seeks to provide an easy path to differential perceptions of students at the upper high school level by applying a story telling method and also, characteristically, to earn some time for class discussion by reducing learning time for simple calculational procedure through Computer Algebra System(CAS) tools. This study offers a cl...
Article
Full-text available
We consider simultaneous solutions of operator Sylvester equations A(i)X - XBi = C-i (1 <= i <= k), where (A(1), ... , A(k)) and (B-1, ... , B-k) are commuting k-tuples of bounded linear operators on Banach spaces epsilon and F, respectively, and (C-1, ... , C-k) is a (compatible) k-tuple of bounded linear operators from F to epsilon, and prove tha...
Article
Full-text available
For over 20 years, the issue of using an adequate CAS tool in teaching and learning of linear algebra has been raised constantly. And a variety of CAS tools were introduced in many linear algebra textbooks. In Korea, however, because of some realistic problems, they have not been introduced in the class and the theoretical aspect of linear algebra...
Article
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Sang-Seol Lee(1870-1917) wrote a manuscript BaekSeungHoCho(百勝胡艸) in the late 19th century. BaekSeungHoCho was transcribed in classical Chinese from the 1879 Japanese book Physics(物理學) by Teizo Ihimori (1851-1916). Sang-Seol Lee, a famous independence activist, is also called Father of the Modern Mathematics Education of Korea, because of his early...
Article
Full-text available
Linear Algebra are arguably the most popular math subjects in colleges. We believe that students' learning and understanding of linear algebra can be improved substantially if we incorporate the latest advanced information technologies in our teaching. We found that the open source mathematics program 'Sage' (http://sagemath.org) can be a good cand...
Article
This paper concerns three notions of matrix functions over semirings; term rank, reduced term rank and star cover number. We compare these matrix functions and we study those linear operators that preserve these matrix functions of n×n symmetric matrices with zero diagonal. In particular, we obtain important characterizations of term-rank (reduced...
Article
Full-text available
This work started with recent students' conception on Linear Algebra. We were trying to help their understanding of Linear Algebra concepts by adding visualization tools. To accomplish this, we have developed most of needed tools for teaching of Linear Algebra class. Visualizing concepts of Linear Algebra is not only an aid for understanding but al...
Article
Full-text available
We consider a three-component reaction-diffusion system with a chemoattraction. The purpose of this work is to analyze the chemotactic effects due to the gradient of the chemotactic sensitivity and the shape of the interface. Conditions for existence of stationary solutions and the Hopf bifurcation in the interfacial problem as the bifurcation para...
Article
Full-text available
Sang-Seol LEE wrote a manuscript HwaHakGyeMongCho(化學啓蒙抄) in the late 19th century. HwaHakGyeMongCho was transcribed from Science Primers: Chemistry (written by H. E. Roscoe), which is translated into Chinese by Joseph Edkins in 1886. LEE did not copy original writing exactly, but he understood the contents of each chapter and sections, then summari...
Article
Full-text available
Given matrices Ai, Bi and Ci of corresponding dimensions over a field , we prove that: (i) if are simultaneously similar to , then there exists a simultaneous solution X to the matrix Sylvester equations ; and (ii) if are simultaneously equivalent to then there exist simultaneous solutions to the matrix equations .
Book
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Contemporary Linear Algebra with Sage (현대 선형대수학 with Sage)
Conference Paper
Full-text available
Over the last 20 years, our learning environment for linear algebra has changed dramatically mathematical tools take an important role in our classes. Sage is popular mathematical software which was released in 2005. This software has efficient features to adapt the internet environment and it can cover most of mathematical problems, for example, a...
Article
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In this paper, we deal with recent researches on Ying N\ddot{u} and Ying Buzu(???) which were addressed in the book Jiu Zhang Suan Shu(????, The Nine Chapters on the Mathematical Art). Ying N\ddot{u}(Ying Buzu) is a concept on profit and loss problems. Ying Buzu Shu(????, the method of excess and deficit) represents an algorithm which has been used...
Article
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Ki-Won Chang(1903-1966) is considered as the first mathematician who made a contribution to the study of the history of Korean mathematics. In this paper, we introduce contributions of Ki-Won Chang, his discovery of old Korean literatures on mathematics, and his academic contribution on the history of Korean mathematics. Then we analyze and compare...
Article
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Until the 1950s, linear algebra was considered only as one of abstract and advanced mathematics subject among in graduate mathematics courses, mainly dealing with module in algebra. Since the 1960s, it has been a main subject in undergraduate mathematics education because matrices has been used all over. In Korea, it was considered as a course only...
Conference Paper
Full-text available
In this research we look for improvements of college mathematics education for enhancing nation's competitive edge, and expose more applicable areas of mathematics. We first investigate current status of mathematics and mathematics education departments of some major universities in the nation. For this, we have sent the survey forms to 20 mathemat...
Article
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We investigate simultaneous solutions of the matrix Sylvester equations AiX-XBi=Ci,i=1,2,…,k, where {A1,…,Ak} and {B1,…,Bk} are k-tuples of commuting matrices of order m×m and p×p, respectively. We show that the matrix Sylvester equations have a unique solution X for every compatible k-tuple of m×p matrices {C1,…,Ck} if and only if the joint spectr...
Article
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A Toeplitz-like matrix has naturally occurred in the construction of iteration functions for finding zeroes of an analytic function. In this note, we study the properties of a Toeplitz-like matrix, and its relationship to the well known Toeplitz matrix involving normalized derivatives of an analytic function.